
theorem
  1193 is prime
proof
  now
    1193 = 2*596 + 1; hence not 2 divides 1193 by NAT_4:9;
    1193 = 3*397 + 2; hence not 3 divides 1193 by NAT_4:9;
    1193 = 5*238 + 3; hence not 5 divides 1193 by NAT_4:9;
    1193 = 7*170 + 3; hence not 7 divides 1193 by NAT_4:9;
    1193 = 11*108 + 5; hence not 11 divides 1193 by NAT_4:9;
    1193 = 13*91 + 10; hence not 13 divides 1193 by NAT_4:9;
    1193 = 17*70 + 3; hence not 17 divides 1193 by NAT_4:9;
    1193 = 19*62 + 15; hence not 19 divides 1193 by NAT_4:9;
    1193 = 23*51 + 20; hence not 23 divides 1193 by NAT_4:9;
    1193 = 29*41 + 4; hence not 29 divides 1193 by NAT_4:9;
    1193 = 31*38 + 15; hence not 31 divides 1193 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1193 & n is prime
  holds not n divides 1193 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
